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Statistical science and interdisciplinary research

Physics in the ‘Once Given’ Universe: New Perspectives on Dynamics, Relativity, Quantum Spectra and the Spin-statistics Connection

C. S. Unnikrishnan

Published Nov 1, 2009• 7 citations
Publisher
DOI
10.1142/9789814287333_0005

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There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations-within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.
Learning quantum mechanics entails adopting a new reference frame for the physical interpretation of the world.The quantum perspective is intrinsically connected with math, which becomes a sort of referent for physical meaning, requiring the employment of new formal structures and a new interpretation of familiar ones.Research evidences that students have difficulty both with concepts and with the use of formalism in qualitative tasks.We administered a 15-item questionnaire focused on incompatibility of observables and related formal structures to 40 physics students of three Italian universities.Semi-structured interviews were scheduled on a subset of students.Results concerning translation processes between math and physical meaning show that most students only look at the square modulus in order to reason on physical information encoded in quantum state, thus neglecting phase relations and their connection with incompatibility.
We develop a structural framework in which physical reality is derived from the spectral properties of quantum states. Within the approach of Universal Modular Dynamics (UMD), the density operator ρ is taken as the fundamental object, and its modular generator K =−log ρ provides a representation of informational content. We show that the distribution of modular energies, defined by the spectrum of K, serves as a primary structure from which higher-level physical organization emerges. In particular, we demonstrate how spectral distributions give rise to stable structures, induce locality through optimal partitioning, and generate geometric relations via correlation-based distances. Dynamics is introduced as an intrinsic ordering of states under modular evolution, while renormalization appears as a spectral phenomenon governed by statistical properties of the modular spectrum. This establishes a connection between informational structure and physical scale. The resulting construction defines a sequential chain of emergence, ρ → p(k) → structure → locality → geometry → dynamics → scale, in which each level arises from properties of the previous one without introducing external assumptions. This work provides a unified perspective in which physical structure is understood as an emergent consequence of spectral information encoded in quantum states.